Francisco Cuevas

Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms

An algorithm for phase demodulation of a single interferogram that may contain closed fringes is presented. This algorithm uses the regularized phase-tracker system as a robust phase estimator, together with a new scanning technique that estimates the phase that initially follows the bright zones of the interferogram. The combination of these two elements constitutes a powerful new method, the fringe-follower regularized phase tracker, that makes it possible to correctly demodulate complex, single-image interferograms for which traditional methods fail.

A parametric method applied to phase recovery from a fringe pattern based on a genetic algorithm

A parametric method to carry out fringe pattern demodulation by means of a genetic algorithm is presented. The phase is approximated by the parametric estimation of an nth-grade polynomial so that no further unwrapping is required. On the other hand, a different parametric function can be chosen according to the prior knowledge of the phase behavior. A population of chromosomes is codified with the parameters of the function that estimates the phase. A fitness function is established to evaluate the chromosomes, which considers: (a) the closeness between the observed fringes and the recovered fringes, (b) the phase smoothness, (c) the prior knowledge of the object as its shape and size. The population of chromosomes evolves until a fitness average threshold is obtained. The method can demodulate noisy fringe patterns and even a one-image closed-fringe pattern successfully.

Modulo 2π fringe orientation angle estimation by phase unwrapping with a regularized phase tracking algorithm

The fringe orientation angle provides useful information for many fringe-pattern-processing techniques. From a single normalized fringe pattern (background suppressed and modulation normalized), the fringe orientation angle can be obtained by computing the irradiance gradient and performing a further arctangent computation. Because of the 180 degrees ambiguity of the fringe direction, the orientation angle computed from the gradient of a single fringe pattern can be determined only modulo pi. Recently, several studies have shown that a reliable determination of the fringe orientation angle modulo 2pi is a key point for a robust demodulation of the phase from a single fringe pattern. We present an algorithm for the computation of the modulo 2pi fringe orientation angle by unwrapping the orientation angle obtained from the gradient computation with a regularized phase tracking method. Simulated as well as experimental results are presented.

A framework for texture classification using the coordinated clusters representation

A statistical approach based on the coordinated clusters representation of images is used for classification and recognition of textured images. The ability of the descriptor to capture spatial statistical features of an image is exploited. A binarization needed for image preprocessing is done using, but not restricted to, a fuzzy clustering algorithm. A normalized spectrum histogram of the coordinated cluster representation is used as a unique feature vector, and a simple minimum distance classifier is used for classification purposes. Using the size and the number of subimages for prototype generation and the size of the test images as the parameters in the learning and recognition phases, we establish the regions of reliable classification in the space of subimage parameters. The results of classification tests show the high performance of the proposed method that may have industrial application for texture classification.

Complex linear filters for phase shifting with very low detuning sensitivity

A new way of synthesizing phase stepping formulae based on linear complex filters is described. These complex linear filters remain in quadrature even for a large amount of detuning (linear phase miscalibration). The linear complex filter is obtained as the minimizer of a quadratic cost functional weighting of several desirable filter properties such as range of quadrature.

A new relative chain code in 3D

A new chain code to represent 3D discrete curves is proposed. The method is based on a search for relative changes in the 3D Euclidean space, composed of three main vectors: a reference vector, a support vector, and a change direction vector, utilized to obtain a directed simple path in a grid of 26 connected components. A set of rotation transformations is defined in the 3D Euclidean space, and an alphabet of only 25 symbols is required to represent any face, edge or vertex-connected discrete curve. Important properties of this code are found: independence under translation, rotation and mirror transformations, as well as high compression levels. A set of 3D curve-skeletons and digital elevation model data to study the terrain were utilized to prove the proposed code. Compared with the state-of-the-art, our method has more advantages: at first, it represents voxelized paths independently of vicinity, also it gives better representation for the tested objects and detects better the redundant parts. This fact is shown in the entropy calculated for 3D curve-skeletons: our method gives 3.03bits/symbol, whereas the state-of-the-art method gives 4.35bits/symbol. On the other hand, our proposed chain code uses 23% less memory than the well known Freeman code of 26 directions. In case of digital elevation models, our method improves memory for 36.1% regarding Freeman code and 10.7% regarding the well known relative code called orthogonal direction change chain code. Finally, average length of the chain code proposed is 14% shorter than the relative code of the state-of-the-art. HighlightsWe defined new rotations to be used to propose a 3D code.Equivalent simple paths allow to save information to be labeled.We found that a set of 25 symbols codify any face, edge and vertex connected 3D path.We applied the new code to a set of skeletons and digital elevation model data.We found invariance under transformations and high compression level of the new 3D code.

Associative Gray Level Pattern Processing using Binary Decomposition and α β Memories

In this note we show how a binary memory can be used to recall gray-level patterns. We take as example the α β associative memories recently proposed in Yáñez, Associative Memories based on order Relations and Binary Operators(In Spanish), PhD Thesis, Center for computing Research, February of 2002, only useful in the binary case. Basically, the idea consists on that given a set of gray-level patterns to be first memorized: (1) Decompose them into their corresponding binary patterns, and (2) Build the corresponding binary associative memory (one memory for each binary layer) with each training pattern set (by layers). A given pattern or a distorted version of it, it is recalled in three steps: (1) Decomposition of the pattern by layers into its binary patterns, (2) Recalling of each one of its binary components, layer by layer also, and (3) Reconstruction of the pattern from the binary patterns already recalled in step 2. The proposed methodology operates at two phases: training and recalling. Conditions for perfect recall of a pattern either from the fundamental set or from a distorted version of one them are also given. Experiments where the efficiency of the proposal is tested are also given.

Object counting without conglomerate separation

Object counting is an important problem in image analysis. All the proposed techniques until now need to split someway the conglomerates of objects in the image before determining their number. The improved technique here proposed uses the skeleton of the image to accomplish the same task. The original technique was first introduced by H. Sossa and G. Guzman (2000). The improved technique also uses the number of terminal points, NTps (points with just one neighbor) and the number of three-edge-points, NTEps (points with just three neighbors) in the skeleton to compute the desired number of objects in the image. The approach is applicable to the case of objects such that when its skeleton is obtained the sum of (NTps+NTEps)=2. The technique can efficiently handle noisy branches in the skeleton and the undesired decomposition of crossing points into three-edge-points normally present when an image is skeletonized. This was not done for the original technique. Both the original and the improved technique are compared in several scenarios.

Path-independent phase unwrapping of subsampled phase maps.

A technique for unwrapping subsampled phase maps is presented. The subsampled phase map is obtained by standard phase-shifting methods that use subsampled interferograms. The technique then estimates the wrapped local curvature of the subsampled phase map. This local curvature is then low-pass filtered with a free-boundary low-pass filter to reduce phase noise. Finally the estimated local curvature of the wave front is integrated by the use of a least-squares technique to obtain the searched continuous wave front.

Demodulation of carrier fringe patterns by the use of non-recursive digital phase locked loop

First- and second-order recursive Digital Phase Locked Loops (DPLLs) have been used recently in fringe data processing because it is the fastest way to obtain the unwrapped phase of a carrier frequency fringe pattern due to its minimal computational overhead. Nevertheless these simple DPLLs cannot cope with fringes having high noise and very wide band phase modulation. In this work we present a highly improved DPLL. The system presented is a non-recursive DPLL which is far more robust than previously presented recursive DPLL. The advantage of this newer technique with respect to recursive DPLL is its higher gain in the signal to noise ratio on the detected phase and higher stability. Unfortunately this is obtained at a higher computational cost.